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Numerical analysis of nonlinear model of excited carrier decay

100%
Tumanova N., Čiegis R., Meilūnas M.
Open Mathematics
|
2013
|
tom 11
|
nr 6
1140-1152
EN
This paper presents a mathematical model for photo-excited carrier decay in a semiconductor. Due to the carrier trapping states and recombination centers in the bandgap, the carrier decay process is defined by the system of nonlinear differential equations. The system of nonlinear ordinary differential equations is approximated by linearized backward Euler scheme. Some a priori estimates of the discrete solution are obtained and the convergence of the linearized backward Euler method is proved. The identifiability analysis of the parameters of deep centers is performed and the fitting of the model to experimental data is done by using the genetic optimization algorithm. Results of numerical experiments are presented.
2
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Another formulation of the Wick’s theorem. Farewell, pairing?

84%
Beloussov I. V.
Special Matrices
|
2015
|
tom 3
|
nr 1
EN
The algebraic formulation of Wick’s theorem that allows one to present the vacuum or thermal averages of the chronological product of an arbitrary number of field operators as a determinant (permanent) of the matrix is proposed. Each element of the matrix is the average of the chronological product of only two operators. This formulation is extremely convenient for practical calculations in quantum field theory, statistical physics, and quantum chemistry by the standard packages of the well known computer algebra systems.
3
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Hybrid fluid-quantum coupling for the simulation of the transport of partially quantized particles in a DG-MOSFET

68%
Jourdana C., Vauchelet N.
Nanoscale Systems: Mathematical Modeling, Theory and Applications
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2015
|
tom 4
|
nr 1
EN
This paper is devoted to numerical simulations of electronic transport in nanoscale semiconductor devices forwhich charged carriers are extremely confined in one direction. In such devices, like DG-MOSFETs, the subband decomposition method is used to reduce the dimensionality of the problem. In the transversal direction electrons are confined and described by a statistical mixture of eigenstates of the Schrödinger operator. In the longitudinal direction, the device is decomposed into a quantum zone (where quantum effects are expected to be large) and a classical zone (where they are negligible). In the largely doped source and drain regions of a DG-MOSFET, the transport is expected to be highly collisional; then a classical transport equation in diffusive regime coupled with the subband decomposition method is used for the modeling, as proposed in N. Ben Abdallah et al. (2006, Proc. Edind. Math. Soc. [7]). In the quantum region, the purely ballistic model presented in Polizzi et al. (2005, J. Comp. Phys. [25]) is used. This work is devoted to the hybrid coupling between these two regions through connection conditions at the interfaces. These conditions have been obtained in order to verify the continuity of the current. A numerical simulation for a DG-MOSFET, with comparison with the classical and quantum model, is provided to illustrate our approach.
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